Details

sample460.0ms

Algorithm

intervals

Results

129.0ms	53×	body	1280	valid
85.0ms	44×	body	640	valid
45.0ms	152×	body	80	valid
22.0ms	19×	body	320	valid
18.0ms	60×	body	80	nan
10.0ms	13×	body	160	valid

simplify940.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	2153
5	683
4	275
3	137
2	81
1	45
0	20

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.1b	(/ (sin B) F)
4.4b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
16.4b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

203×	`times-frac`
143×	`*-un-lft-identity`
113×	`add-sqr-sqrt` `add-cube-cbrt`
60×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`distribute-lft-out` `sqr-pow`
14×	`associate-/l*`
13×	`add-cbrt-cube`
12×	`div-inv`
11×	`div-exp`
5×	`pow1` `cbrt-undiv`
4×	`insert-posit16` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `clear-num` `frac-2neg` `pow-exp`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot`

Counts

4 → 221

Calls

4 calls:

5.0ms	(/ x (tan B))
8.0ms	(/ (sin B) F)
87.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
40.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series738.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ x (tan B))
43.0ms	(/ (sin B) F)
267.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (/ (sin B) F))
302.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify1.5s

Counts

233 → 233

Iterations

Iter	Nodes
2	2537
1	920
0	396

prune3.5s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.9b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ x (tan B))
0.3b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
0.3b	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
16.4b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite305.0ms

Algorithm

rewrite-expression-head

Rules

994×	`times-frac`
538×	`*-un-lft-identity`
444×	`add-sqr-sqrt` `add-cube-cbrt`
188×	`unpow-prod-down`
56×	`add-exp-log`
47×	`distribute-lft-out` `sqr-pow`
46×	`div-inv`
40×	`div-exp`
39×	`associate-/l*`
20×	`add-cbrt-cube`
19×	`associate-/r*`
10×	`cbrt-undiv`
6×	`pow-to-exp` `pow-exp`
5×	`pow1`
4×	`rec-exp` `1-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot` `associate-/l/`

Counts

4 → 536

Calls

4 calls:

5.0ms	(/ x (tan B))
104.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
122.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
54.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series831.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ x (tan B))
180.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
219.0ms	(/ (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)) (/ 1 F))
293.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify3.6s

Counts

548 → 548

Iterations

Iter	Nodes
1	2382
0	828

prune9.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.9b

localize56.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 F) (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)))
0.3b	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
0.4b	(/ 1 (/ (/ 1 F) (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))))
16.4b	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

rewrite477.0ms

Algorithm

rewrite-expression-head

Rules

5804×	`times-frac`
2780×	`*-un-lft-identity`
2374×	`add-sqr-sqrt` `add-cube-cbrt`
812×	`unpow-prod-down`
400×	`associate-/r*`
214×	`div-inv`
206×	`add-exp-log`
203×	`distribute-lft-out` `sqr-pow`
181×	`div-exp`
36×	`add-cbrt-cube`
33×	`rec-exp` `1-exp`
24×	`associate-/l*`
22×	`cbrt-undiv`
18×	`pow-to-exp` `pow-exp`
6×	`pow1` `associate-/r/`
4×	`insert-posit16` `add-log-exp`
3×	`pow-unpow` `clear-num` `frac-2neg`
1×	`pow-pow` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 2056

Calls

4 calls:

76.0ms	(/ (/ 1 F) (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)))
119.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
97.0ms	(/ 1 (/ (/ 1 F) (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))))
59.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

series851.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (/ 1 F) (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B)))
201.0ms	(/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))
204.0ms	(/ 1 (/ (/ 1 F) (/ (pow (+ (+ (* 2 x) (* F F)) 2) -1/2) (sin B))))
300.0ms	(pow (+ (+ (* 2 x) (* F F)) 2) -1/2)

simplify5.0m

Counts

2068 → 2068

Iterations

Iter	Nodes
1	7438
0	2443

prune37.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (sin B)) (/ 1 F))
1.9b	(* (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (/ (/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (sin B)) (/ 1 F)))
16.4b	(sqrt (+ (+ (* 2 x) (* F F)) 2))
16.4b	(sqrt (+ (+ (* 2 x) (* F F)) 2))

rewrite482.0ms

Algorithm

rewrite-expression-head

Rules

2676×	`times-frac`
1332×	`add-sqr-sqrt`
1290×	`*-un-lft-identity`
1102×	`add-cube-cbrt`
630×	`unpow-prod-down`
486×	`associate-r`
364×	`sqrt-prod`
217×	`add-exp-log`
144×	`div-exp`
110×	`sqr-pow`
104×	`div-inv`
84×	`distribute-lft-out`
64×	`unswap-sqr`
51×	`prod-exp`
37×	`associate-/l*`
34×	`add-cbrt-cube`
33×	`pow-to-exp` `pow-exp`
16×	`cbrt-undiv` `rec-exp` `1-exp`
13×	`associate-/r*`
11×	`associate-l`
6×	`pow1`
5×	`cbrt-unprod`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip-+`
1×	`clear-num` `frac-2neg` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 1225

Calls

4 calls:

97.0ms	(/ (/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (sin B)) (/ 1 F))
262.0ms	(* (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (/ (/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (sin B)) (/ 1 F)))
28.0ms	(sqrt (+ (+ (* 2 x) (* F F)) 2))
35.0ms	(sqrt (+ (+ (* 2 x) (* F F)) 2))

series1.0s

Counts

4 → 12

Calls

4 calls:

521.0ms	(/ (/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (sin B)) (/ 1 F))
194.0ms	(* (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (/ (/ (pow (sqrt (+ (+ (* 2 x) (* F F)) 2)) -1/2) (sin B)) (/ 1 F)))
139.0ms	(sqrt (+ (+ (* 2 x) (* F F)) 2))
187.0ms	(sqrt (+ (+ (* 2 x) (* F F)) 2))

simplify8.0s

Counts

1237 → 1237

Iterations

Iter	Nodes
1	4558
0	1384

prune25.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes311.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 11.8b

bsearch643.0ms

Steps

Iters	Range		Point
10	2.0771527274346896e+27	4.0128945167102486e+38	2.0998209165392296e+27
9	-197961822148.07825	-338862.1189523287	-172717042.99853888

simplify8.0ms

Iterations

Iter	Nodes
3	45
2	45
1	42
0	34

end0.0ms

sample11.8s

Algorithm

intervals

Results

4.4s	1641×	body	1280	valid
2.9s	1416×	body	640	valid
2.3s	4812×	body	80	valid
901.0ms	702×	body	320	valid
610.0ms	1656×	body	80	nan
262.0ms	341×	body	160	valid